Straightforward problems: My students expect problems to always be short, with only one idea in play.That presumably reflects that in high school, problems were always rigged so that the quadratic would factor. For example, my students can actually factor quadratics on sight very well (better than I can), but aren't very comfortable with the quadratic formula (to the point that some of them don't remember having seen it). I notice that my students are sometimes uncomfortable with answers that aren't very 'clean'.

Streamlined problems: To accommodate the previous item, high school courses seem to primarily give problems where the algebra is simple.Even when students can eventually do the algebra, it's slow and difficult for them for instance, I notice that some of my students have trouble learning calculus because they get distracted by the algebra - it takes them forever and they have to spend a lot of time thinking about it, so they can't focus as much on the new material. Calculus courses, on the other hand, often work with problems that assume students can reliably do algebra. Pre-calc preparation: High schools are under a lot of pressure to push students through calculus, so they often skimp on algebra and trigonometry.I've seen students who rely on their notes leave out whole sections of class because we spent half an hour on an idea rather than a formula, and they didn't see anything in it worth writing down.

I think it also has an indirect effect: students have learned that formulas are what math is, and some of them have learned to tune out anything other than formulas. That has some direct effects - students struggle with figuring out how to apply formulas which are more abstract (like the definition of the derivative), and aren't prepared for problems which call for a non-algorithmic decision about which formula to use. Reliance on formulas: As you noticed, a lot of high schools teach calculus in way that's overly reliant on formulas.I've noticed a number of ways that my students' high school courses seem to cause them trouble in college: The pressure to get students through that with an adequate success rate seems to have lead to some streamlining and cutting corners in ways that mean that what gets taught doesn't really stick, and also doesn't set students up for success when they retake calculus in college. But at the same time, I doubt this can account for the huge disparity in performance between I would expect from a student who took high school calculus and what I see.Īssuming we're talking about mostly US students, most American high schools teach calculus in a way that's very focused on the AP test. Which leads me to believe that at least some high school curricula teach very little of the underlying math and teach calculus as a bunch of formulas.

One observation I have made is that the students who take calculus in high school are very reliant on formulas: I think those that struggle at the college level find it, for example, hard to apply the definition of the limit to actually derive a derivative.

They learn and apply some of the standard theorems and definitions (continuity, IVT, Extreme Value Theorem, MVT, FTC).

They develop an understanding of what an integral and derivative mean mathematically by applying the limiting processes along within a geometric setting to a few simple power functions.

They learn how to take limits (but we do not do delta-epsilon proofs).

They learn to 'translate' word problems into mathematical problems they can solve with the tools of calculus (esp problems involving physics and engineering applications).

They learn to use the traditional 'plug and chug' formulas for differentiation and integration.

With the one qualifier that we do not allow our students to use advanced calculators that can do graphing or symbolic manipulation on our exams, I would characterize our calculus 1 class as a pretty standard typical one where students focus on 5 main areas: To give you a bit more context about my situation, my institution is a moderately competitive engineering school that offers a 3 sequence calculus class that is mandatory for our engineers. Is there such variance among what constitutes 'calculus' in high school curriculum or that big a difference between high school and college calculus? I am an instructor at an engineering college and I've noticed a decent number of students who have calculus 1 on their high school transcript and yet fail abysmally at the college level. I am curious why students who take calculus in high school often do so poorly in college calculus.

Difference between ab and bc calculus